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Consensus latent incomplete multi-view clustering with low-rank tensor constraint

INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2023年第11期14卷 3813-3825页

作者： Ji, Guangyan Lu, Gui-Fu Anhui Polytech Univ Sch Comp & Informat Wuhu 241000 Anhui Peoples R China

Traditional multi-view clustering (MVC) assumes that all views are complete and it cannot address a lack of views. In real life, a lack of views often occurs, thus leading to the problem of incomplete MVC (IMVC). Although the existing IMVC methods have achieved good performance, they have the following weaknesses. (1) The completion method is not flexible enough for the case where view information is arbitrarily missing. (2) They fail to adequately explore the higher-order correlations among views. (3) The cluster structure of the input data is not considered. Thus, to solve these problems, in this paper, we propose a novel method, i.e., consensus latent incomplete multi-view clustering with low-rank tensor constraint (CLIMVC/LTC). Specifically, we first use a latent model to generate the missing views to make the completion process more flexible. Then, we utilize the low-rank tensor constraint and consensus representation term to jointly explore the higher-order correlations, the cluster structure of the data and the consistency between different views. That is, CLIMVC/LTC combines missing view completion, which is implemented by a latent model, low-rank tensor constraint and consensus representation learning into a unified framework, and their interaction yields improved clustering performance. An optimization procedure based on the augmented Lagrange multiplier (ALM) method is also designed to solve CLIMVC/LTC. The effectiveness of CLIMVC/LTC is verified on several well-known datasets, and it has good clustering performance.

关键词： IMVC low-rank tensor constraint Consensus representation learning Latent model

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Robust high-order graph learning for incomplete multi-view clustering

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 280卷

作者： Wang, Daoyuan Ren, Fujian Zhuang, Yuntang Liang, Cheng Shandong Normal Univ Sch Informat Sci & Engn Jinan 250358 Shandong Peoples R China

Incomplete multi-view clustering is a challenging problem in unsupervised learning that involves grouping multi-view data with missing information into distinct clusters. In this study, we propose a novel robust high-order graph learning (RHGL) method for incomplete multi-view clustering. Specifically, a robust principal component analysis is first employed to gain error-free matrices based on the original available data and then the obtained robust representations are utilized for local manifold learning. Next, we align the view-specific partitions generated from the local similarity structures and perform complete similarity graph learning to explore the global similarity structure. To capture the high-order relationships among views, all complete similarity graphs are stacked into a third-order tensor with the low-rank constraint. As a result, our model can simultaneously explore both local and global similarity structures and mine high-order inter-view correlations. An effective iterative optimization strategy is developed to solve the proposed approach. Experiments on six benchmark datasets show that our model outperforms the competing methods.

关键词： Incomplete multi-view clustering Graph learning Partition learning low-rank tensor constraint

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tensorized Scaled Simplex Representation for Multi-View Clustering

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IEEE TRANSACTIONS ON MULTIMEDIA 2024年 26卷 6621-6631页

作者： Cai, Bing Lu, Gui-Fu Li, Hua Song, Weihong Anhui Inst Informat Technol Sch Comp & Software Engn Wuhu 241000 Peoples R China Anhui Polytech Univ Sch Comp & Informat Wuhu 241000 Peoples R China

tensor-based multi-view clustering, which incorporates high-order correlations among views, has emerged as a promising research direction. These methods aim to capture intrinsic structure through a tensor-based constraint and then construct an affinity matrix. However, when constructing the affinity matrix, the negative entries in the coefficient matrices are forced to be positive via absolute operation, which can inadvertently destroy the inherent relationships within the data. Furthermore, existing methods may lack the flexibility to effectively handle and fuse multiple views. To address these issues, we propose a novel approach called tensorized Scaled Simplex Representation (TSSR) for multi-view clustering. TSSR leverages a low-rank tensor constraint to capture the consensus and complementary information among the views. Besides, it introduces the scaled simplex representation, ensuring non-negative coefficient matrices, thus preserving inherent relationships and enhancing flexibility. Thirdly, TSSR extends the scaling range of the affine constraint to capture authentic structural information. Finally, an auto-weighted strategy assigns ideal weights to diverse views, enabling them to contribute appropriately. We integrate these techniques into a unified framework solved by an iterative algorithm. Experimental results demonstrate that TSSR outperforms state-of-the-art methods in terms of performance and efficiency.

关键词： Scaled simplex representation low-rank tensor constraint adaptive weights multi-view clustering

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Twin Reciprocal Completion for Incomplete Multi-View Clustering

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 2024年第12期34卷 13201-13212页

作者： Zheng, Qinghai Tang, Haoyu Shandong Univ Sch Software Jinan 250101 Peoples R China Fuzhou Univ Coll Comp & Data Sci Fuzhou 350108 Peoples R China

Incomplete multi-view clustering is an important and challenging task, which has attracted significant attention in recent years. The key objective of incomplete multi-view clustering is to excavate the underlying avaliable consistency of multi-view data, so as to enable the effective reconstruction of missing views for clustering. In this paper, we introduce a completion framework that deeply explores the underlying consistency and effectively completes the missing views. Following that, we propose a novel Twin Reciprocal Completion for Incomplete multi-view clustering, termed TRC-IMC for short. To be specific, TRC-IMC jointly conducts the Completion in Feature space (CF) and the Completion in Subspace (CS) to reciprocally complete the data with missing views. The underlying high-order consistency of multi-view data can be fully explored in both the feature space and subspace to guide the completion process of missing views. Extensive experiments are conducted on eight real-world multi-view datasets, and experimental results indicate the promising performance of our method, compared to several state-of-the-arts.

关键词： tensors Excavation Task analysis Kernel Clustering methods Circuits and systems Vectors Incomplete multi-view data subspace clustering low-rank tensor constraint

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Multiple kernel-based anchor graph coupled low-rank tensor learning for incomplete multi-view clustering

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APPLIED INTELLIGENCE 2023年第4期53卷 3687-3712页

作者： Wang, Senhong Cao, Jiangzhong Lei, Fangyuan Jiang, Jianjian Dai, Qingyun Ling, Bingo Wing-Kuen Guangdong Univ Technol Sch Informat Engn Guangzhou 510006 Peoples R China Guangdong Polytech Normal Univ Guangdong Prov Key Lab Intellectual Property & Bi Guangzhou 510006 Peoples R China

Incomplete Multi-View Clustering (IMVC) attempts to give an optimal clustering solution for incomplete multi-view data that suffer from missing instances in certain views. However, most existing IMVC methods still have various drawbacks in practical applications, such as arbitrary incomplete scenarios cannot be handled;the computational cost is relatively high;most valuable nonlinear relations among samples are often ignored;complementary information among views is not sufficiently exploited. To address the above issues, in this paper, we present a novel and flexible unified graph learning framework, called Multiple Kernel-based Anchor Graph coupled low-rank tensor learning for Incomplete Multi-View Clustering (MKAGT_IMVC), whose goal is to adaptively learn the optimal unified similarity matrix from all incomplete views. Specifically, according to the characteristics of incomplete multi-view data, MKAGT_IMVC innovatively improves an anchor selection strategy. Then, a novel cross-view anchor graph fusion mechanism is introduced to construct multiple fused complete anchor graphs, which captures more the intra-view and inter-view nonlinear relations. Moreover, a graph learning model combining low-rank tensor constraint and consensus graph constraint is developed, where all fused complete anchor graphs are regarded as prior knowledge to initialize this model. Extensive experiments conducted on eight incomplete multi-view datasets clearly show that our method delivers superior performance relative to some state-of-the-art methods in terms of clustering ability and time-consuming.

关键词： Incomplete multi-view clustering Anchor graph Multiple kernel low-rank tensor constraint Consensus graph constraint

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One-step incomplete multiview clustering with low-rank tensor graph learning

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INFORMATION SCIENCES 2022年 615卷 209-225页

作者： Ji, Guangyan Lu, Gui-Fu Anhui Polytech Univ Sch Comp & Informat Wuhu 241000 Anhui Peoples R China

Incomplete multiview clustering (IMVC) has attracted extensive attention in the field of machine learning due to its excellent performance in handling incomplete multiview data (IMVD). However, existing IMVC methods often use spectral clustering or k-means on the obtained affinity matrices to obtain the final clustering results, that is, the affinity matrices learning process and clustering process are separated. In this paper, we propose a new ingenious IMVC method, one-step incomplete multiview clustering with low-rank tensor graph learning (OIMVC/LTGL), to solve the problem. This method combines graph learning, low-rank tensor constraint, common representation learning and clustering into a unified optimization framework. First, we utilize the adjacency relationship between views to complete the similarity graph matrices. Second, we stack all similarity graph matrices into a third-order tensor. To mine higher-order correlations among different views, we impose a low-rank tensor constraint, the tensor nuclear norm (TNN), into the constructed tensor. Third, to explore consistent information between views, we introduce a common represen-tation learning term to learn the optimal consensus representation. Last, we introduce spectral rotation to the consensus representation matrices to directly obtain the clustering labels. These steps promote each other for better clustering performance. We solve the optimization problem by using the augmented Lagrange multiplier (ALM) method. Experiments based on five well-known datasets show the superiority of our method.(c) 2022 Elsevier Inc. All rights reserved.

关键词： One-step IMVC low-rank tensor constraint Graph learning Common representation learning Spectral rotation

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Multi-view subspace clustering via slack consistency and double-side orthogonal diversity

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 277卷

作者： Luo, Yixuan Ma, Wenming Liu, Shudong Tong, Xiangrong Du, Xiaolin Liu, Zhaowei Li, Mingqi Jiang, Hongwei Yantai Univ Sch Comp & Control Engn Yantai 264005 Peoples R China Zhongnan Univ Econ & Law Sch Informat Engn Wuhan 2430073 Peoples R China

Multi-view subspace clustering is a powerful technique for handling high-dimensional data and effectively reducing dimensionality. However, current multi-view subspace clustering methods encounter two significant challenges. First, they heavily rely on the self-representation matrix to extract consistency information between views, which may introduce noise and lead to overly constrained consistency matrices. Second, existing methods struggle to balance consistency and complementarity in multi-view clustering. To address these issues, we propose a novel multi-view subspace clustering approach based on slack consistency and double- side orthogonal diversity (SCDOD). Our method introduces a set of slack consistency matrices that bridge the self-representation matrix and the global consistency matrix. Through global consistency constraints, we obtain global consistency information while mitigating constraints typically associated with global consistency construction. Additionally, our approach incorporates double-side orthogonal diversity, enhancing diversity between the slack consistency matrices and specificity matrices, as well as among the specificity matrices themselves. This effectively explores the complementarity of different data views. Experimental results on several real-world datasets demonstrate the effectiveness of our proposed method.

关键词： Multi-view subspace clustering low-rank tensor constraint Orthogonal diversity Slack consistency

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View-specific anchors coupled tensorial bipartite graph learning for incomplete multi-view clustering

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INFORMATION SCIENCES 2024年 664卷

作者： Han, Xuemei Zhou, Fei Ren, Zhenwen Wang, Xueyuan You, Xiaojian Southwest Univ Sci & Technol Sch Informat Engn Mianyang 621010 Peoples R China Guangxi Informat Ctr Joint Innovat Lab Digital GuangXi Smart Infrastru Nanning 530000 Peoples R China Wuzhou Univ Guangxi Key Lab Machine Vis & Intelligent Control Wuzhou 543002 Guangxi Peoples R China

The incomplete multi -view clustering (IMVC) aims to explore the consensus and complementary information embedded in incomplete multi -view data, so as to accurately aggregate all samples into different clusters. Existing IMVC methods still have the following issues that need to be further solved: how to efficiently (1) alleviate the computational complexity;(2) capture the complementary information from views;(3) uncover the high -order correlations underlying incomplete multi -view data. To address these problems, a new method, called view -specific anchors coupled tensorial bipartite graph learning for incomplete multi -view clustering (VATBGIMC), is proposed in this paper. Specifically, view -specific anchors are learned from nonmissing samples to represent the distribution of all samples including missing ones. With the help of high -quality anchors, the bipartite graph between all samples and anchors is constructed, which can preserve the complementary information. Meanwhile, these bipartite graphs are stacked into a tensor which is imposed with a low -rank constraint to adequately capture the inter -view and inter -sample correlations from incomplete multi -view data. Further, the augmented graph of bipartite graph is constrained by Laplacian rank to learn a consensus cluster indicator. A large number of experiments validate the superiority and efficiency of the proposed method in terms of clustering performance and time consumption.

关键词： Incomplete multi-view clustering Bipartite graph learning High-order correlations low-rank tensor constraint

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